Bose-Einstein condensation (BEC) in dilute gases stands as a fascinating phenomenon of quantum mechanics. In this state, hundreds of thousands of atoms occupy the lowest energy level, establishing a collective macroscopic quantum state, with numerous intriguing properties. BEC has become a fundamental tool for the exploration of quantum physics and it may facilitate further advancements in quantum technology, for instance, in quantum simulation and sensing applications. Due to the potential of BECs in both basic research and technology, a fundamental understanding of this phenomenon is essential to guarantee the precision and reliability of its applications. Atom number fluctuations in BECs stand as an unresolved fundamental problem that has posed significant theoretical challenges for nearly eight decades. The experimental observation of this effect has recently become feasible. However, a direct comparison between theoretical predictions and experimental results remains outstanding. In particular, technical challenges persist in the accurate detection of the BEC, and a thorough understanding of estimation errors is lacking. This PhD thesis addresses some of these challenges in the field. Firstly, it introduces an enhanced calibration method for time-of-flight absorption images of ultracold atomic clouds, improving the accuracy of such measurements. Additionally, a thorough statistical analysis of uncertainties in the preparation and parameter estimation of partially condensed Bose gases is presented, leading to an improved understanding of atom number fluctuations in BEC. Finally, this thesis presents the experimental advances toward a new project within the research group: Electromagnetically induced transparency (EIT). EIT is a concept where an otherwise opaque cloud can be made transparent through manipulation of its quantum states. Notably, these advancements include the construction of setups for an optical dipole trap and a hybrid trap, along with the development of systems enabling precise control of magnetic fields. This laid the groundwork for recent demonstrations of EIT within the group.
Bose-Einstein condensation (BEC) in dilute gases stands as a fascinating phenomenon of quantum mechanics. In this state, hundreds of thousands of atoms occupy the lowest energy level, establishing a collective macroscopic quantum state, with numerous intriguing properties. BEC has become a fundamental tool for the exploration of quantum physics and it may facilitate further advancements in quantum technology, for instance, in quantum simulation and sensing applications. Due to the potential of BECs in both basic research and technology, a fundamental understanding of this phenomenon is essential to guarantee the precision and reliability of its applications. Atom number fluctuations in BECs stand as an unresolved fundamental problem that has posed significant theoretical challenges for nearly eight decades. The experimental observation of this effect has recently become feasible. However, a direct comparison between theoretical predictions and experimental results remains outstanding. In particular, technical challenges persist in the accurate detection of the BEC, and a thorough understanding of estimation errors is lacking. This PhD thesis addresses some of these challenges in the field. Firstly, it introduces an enhanced calibration method for time-of-flight absorption images of ultracold atomic clouds, improving the accuracy of such measurements. Additionally, a thorough statistical analysis of uncertainties in the preparation and parameter estimation of partially condensed Bose gases is presented, leading to an improved understanding of atom number fluctuations in BEC. Finally, this thesis presents the experimental advances toward a new project within the research group: Electromagnetically induced transparency (EIT). EIT is a concept where an otherwise opaque cloud can be made transparent through manipulation of its quantum states. Notably, these advancements include the construction of setups for an optical dipole trap and a hybrid trap, along with the development of systems enabling precise control of magnetic fields. This laid the groundwork for recent demonstrations of EIT within the group.
Abstract The investigation of atom number fluctuations in quantum gases at finite temperatures showcases the ongoing challenges in understanding complex quantum systems. Recently, the microcanonical nature of atom number fluctuations in weakly interacting Bose–Einstein condensates was observed. This motivates an investigation of the thermal component of partially condensed Bose gases, due to the conservation of the total atom number. Here, we present a combined analysis of both components, including a comprehensive analysis of the uncertainties in the preparation and parameter extraction of partially condensed quantum gases. This enables a complementary observation of the thermal atom number fluctuations and yields and improved value of the peak BEC atom number fluctuations Δ N p , 0 2 = ( 3.7 ± 7 ) × 10 5 close to the critical temperature. This corresponds to a reduction by 41% with respect to previous analysis and corroborates the microcanonical nature of the fluctuations. The analysis of noise contributions due to the preparation and evaluation of partially condensed Bose gases is based on Monte Carlo simulations of optical density profiles. Importantly, this allows for an estimation of the technical noise contributions to the atom number and temperature, which is generally applicable in the field of ultracold atoms.
Bose-Einstein condensates (BECs), a quantum state of matter formed when bosonic atoms are cooled close to absolute zero, have become the premier platform for investigating fundamental physics with atomic vapours. Experiments on Bose-Einstein condensates now achieve exquisite control over many aspects of the system, including interactions, trapping potential, and dynamics. This has precipitated a new wave of research into many-body quantum phenomena and, in particular, solitons. These structures are fundamental excitations of an interacting non-linear medium, of interest to a multitude of scientific disciplines from non-linear optics to financial markets. The highly controllable environment of BECs form an attractive playground for the study of solitons allowing the non-linearity to be dynamically tuned, facilitating deeper investigations into these structures. Consistently generating and analysing solitons in BEC experiments continues to be problematic. In particular, the non-linear dynamics of BECs, though required for the generation of solitons, produce particularly challenging control and optimization problems. These control problems must be solved before further investigations into the fundamental physics of soliton dynamics can be answered. This thesis makes three important advances in the control and measurement of BECs that will lead to better generation and observation of solitons. (1) a theoretical model for a control scheme capable of highly precise wavefunction engineering, (2) the experimental implementation of a machine learning algorithm for online optimisation, and (3) a continuous non-destructive imaging system capable of directly observing soliton dynamics in real-time. Together, these advances provide a suite of tools for manipulating and exploiting solitons in Bose-Einstein condensates. A novel technique was developed theoretically, offering control of the macroscopic wavefunction of a Bose-Einstein condensate with unprecedented spatial resolution and speed. The ability to control the atomic wavefunction at the fundamental length scale is key to the advancement of many quantum technologies such as quantum simulators. The magnetic resonance control scheme is demonstrated through simulation of a 87Rb condensate with the exemplar model generating a single dark soliton with corresponding π phase kink. The soliton represents a structure at the fundamental length scale of the system, and demonstrates the potential of the scheme for precision state engineering. The scheme is extended to generate higher-order soliton modes which are yet to be experimentally realised. A machine learning algorithm based on Gaussian processes was developed and implemented on the evaporative cooling stage of the production of a 87Rb Bose-Einstein condensate, successfully demonstrating fast optimisation to condensation. The Gaussian process develops a statistical model based on the data that enables the characterisation of the relationship between the experimental controls and resultant quality of the BEC. This relationship is often obfuscated through technical details of the apparatus, frustrating the use of theoretical models to design optimal evaporation ramps. These models often only consider ergodic dynamics with two-body s-wave interactions and no other loss rates with better ramps likely exploiting more complex interactions. The internal model generated from the Gaussian process utilised uncertainty in measured data, making the optimisation more robust to experimental noise than alternate methods. The algorithm is shown to produce high quality Bose-Einstein condensates in 10 times fewer experimental iterations than previously used online optimisation techniques. By exploiting information on the sensitivity of each control, the model can be used to aid experimental design. The convergence of the optimisation is further improved by eliminating a superfluous parameter identified by the model. The general usefulness of machine learning compared with bespoke optimisation algorithms has seen machine learning approach ubiquity. Finally, an experimentally straightforward technique for continuous non-destructive imaging of matter-wave solitons was developed and implemented, facilitating measurements of stochastic phenomena. The technique is readily practicable on any ultracold atom experiment with an existing absorption imaging system, simply requiring the probe laser be far-detuned from resonance. With a signal-to-noise of ∼ 33 at 1.25 GHz detuning, the technique is capable of producing 100 images with no observable heating or atom loss. Coupled with a fast optical phase locked loop, the technique can be used in conjunction with absorption imaging to generate a series of non-destructive images followed by a final high signal-to-noise absorption image solely through moving the laser on resonance for the final image. The high performance and utility of this imaging setup make it a powerful tool for ultra-cold atom experiments.
Bose-Einstein condensation (BEC) represents a remarkable phase transition, characterized by the formation of a single quantum subsystem. As a result, the statistical properties of the condensate are highly unique. In the case of a Bose gas, while the mean number of condensed atoms is independent of the choice of statistical ensemble, the microcanonical, canonical (CN), or grand CN (GC) variances differ significantly among these ensembles. In this paper, we review the progress made over the past 30 years in studying the statistical fluctuations of BECs. Focusing primarily on the ideal Bose gas, we emphasize the inequivalence of the Gibbs statistical ensembles and examine various approaches to this problem. These approaches include explicit analytic results for primarily one-dimensional systems, methods based on recurrence relations, asymptotic results for large numbers of particles, techniques derived from laser theory, and methods involving the construction of statistical ensembles via stochastic processes, such as the Metropolis algorithm. We also discuss the less thoroughly resolved problem of the statistical behavior of weakly interacting Bose gases. In particular, we elaborate on our stochastic approach, known as the hybrid sampling method. The experimental aspect of this field has gained renewed interest, especially following groundbreaking recent measurements of condensate fluctuations. These advancements were enabled by unprecedented control over the total number of atoms in each experimental realization. Additionally, we discuss the fluctuations in photonic condensates as an illustrative example of GC fluctuations. Finally, we briefly consider the future directions for research in the field of condensate statistics.
In the years following the first Bose-Einstein condensation of dilute atomic gases in 1995, several experiments demonstrated many fundamental properties of two-component BEC. Subsequent to these pioneering experiments, almost a decade passed with little experimental activity, relative to investigations of single-component condensates. In somewhat of a renaissance, the initial observations of two-component BEC have been revisited in recent years, consolidating and clarifying results of the early works, and illuminating new and surprising behaviour of these rich quantum fluids. This thesis presents new experimental results on the relative phase evolution of two-component Bose-Einstein condensates (BECs). We approach our study of this system from the dual perspective of binary superfluidity and trapped atom interferometry. We observe nonequilibrium dynamics of the condensate that are deeply connected to the physics of interpenetrating superfluids. These dynamics have consequences for interferometers whose two paths are different internal spin states of the condensate atoms. Using trapped condensates for precision measurement draws upon the benefits of confined atom interferometry - long interrogation times, precise position control to measure near-field potentials - in addition to the unique coherence properties of BECs. Precision measurementwith trapped particles, however, is obstructed by the inherent inhomogeneities associated with the confinement itself. Spatial variation of the external potentials and atomic density can give rise to dephasing during the free evolution and imperfect splitting and recombination of the interferometric paths. In this thesis, we consider the dephasing of the two-componentmean field order parameter, which tends to diminish the interference signal attained with the condensate. The promise of fuhs for atom interferometry lies within using nonclassical many body states to reduce the fundamental noise limit imposed upon measuring the projection of atomic pseudospin. Before the many body quantum properties of two-component condensates can be used to their full potential, the ideal classical limit must be achieved and investigated. As in optical interferometry, the classical ideality of an interference measurement is contingent upon control of the spatialmodes - thematter wave fields, or single particle wave functions. Whilst much attention is currently focused on preparing nonclassical many body states for entanglement and squeezing of the condensate pseudospin, this thesis focuses on the ancillary yet important issue of spatial inhomogeneity of the condensate mean field. Reversal of the spatially inhomogeneous mean field evolution is demonstrated, employing the techniques of nuclear magnetic resonance. A new method is demonstrated to probe pseudospin -1/2 condensates involving microwave adiabatic passage. The technique permits simultaneous, spatially resolved absorption imaging of the spatial mode of each component. Controlled manipulation of the components into Zeeman states with different magnetic moments allows spatial separation using a Stern-Gerlach separation technique, providing a spatially resolved projection of the local condensate pseudospin from a single absorption image. We propose an interferometric technique which employs this imaging method to directly image the relative phase. The miscibility of the two components depends on the relative magnitude of the interactions between various collision partners. The boundary of this miscibility is found to be less pronounced than expected from the commonly applied results of homogeneous super-fluids.The effects of kinetic energy are shown to be significant at the threshold of miscibility, leading to a breakdown in the Thomas-Fermi approximation. Magnetic dipole transitions amongst alkali ground states are often used to prepare, manipulate, and interrogate pseudospin -1/2 condensates. We present a thorough investigation of the two-photonmagnetic dipole transitions between the |F = 1,mF = -1〉 and |F = 2,mF = +1〉 states, and the |F = 1,mF = +1〉 and |F = 2,mF = -1〉 states of 87Rb. Taking into account all 8 Zeeman levels of the electronic ground state reveals markedly different radiative shifts and effects beyond the rotating wave approximation, compared to the three-level formalism commonly used for these transitions.This has implications for Ramsey interferometry using the two-photon magnetic dipole transitions. The unchartered experimental territory offered by two-component condensates is vast, and future directions, supplementary to the work in this thesis, are elucidated.
Research on degenerate quantum gases of dilute atomic gases has become a well established field in modern physics and revealed many astonishing phenomena. The first experiments on Bose and Fermi gases at low temperatures aimed to prove the predictions of quantum mechanics on a macroscopic scale. Since then we make use of Bose and Fermi gases and mixtures of any combination to model other many body systems. A property of Bose Einstein condensates is superfluidity which we want to investigate further in toroidal potentials with a new apparatus which can produce an all-optical BEC. This means trapping thermal atoms in an optical dipole trap and cooling the sample by evaporation into the quantum degenerate regime. This new technique was first successfully demonstrated by M.D. Barrett et al. in 2001 and promises to be faster and simpler than the well established and common way of evaporation in magnetic traps. A new apparatus was built by the author and we report on the experimental details of the trapping of 87Rb atoms from a hot vapour and cooling them in a magneto-optical trap, and further evaporation to quantum degeneracy in a crossed optical dipole trap operating at a wavelength of l = 1064nm, with accurate control of the power in both beams via a feedback loop. The evaporation of neutral atoms of 87Rb in far red detuned optical dipole traps using linearly polarised laser light is spin independent, and mixed spinor condensates of the F=1 manifold can be formed. As an empirical technique we found by applying a magnetic gradient field during the final evaporation that we can selectively populate mF spin states or prepare mixtures. This intriguing mechanism was found earlier as well by M. S. Chang, but is yet not fully understood and subject of our future research. We can now routinely prepare an almost pure condensate containing up to 7000 atoms in the condensed phase purely in the mF = 0 spin state. This thesis contains the theoretical framework of Bose-Einstein condensation with in mean-field theory, the concepts of cooling of atoms in magneto-optical traps, the trapping and evaporation in optical dipole traps and the experimental realisation. In the future this experiment will be extended by a fast scanning dipole trap to apply arbitrary time averaged potentials of more complex geometries, such as toroidal traps to study the effects of superfluidity in a periodic potential. The production of toroidal traps and cold atoms in such a trap are outlined in this thesis.
Turbulence appears in most natural and man-made flows. However, the analysis of turbulence is particularly difficult. Links between microscopic fluid dynamics and statistical signatures of turbulence appear unobtainable from the postulates of fluid dynamics making turbulence one of the most important unsolved theoretical problems in physics. Two-dimensional quantum turbulence (2DQT), an emerging field of study, involves turbulence in two-dimensional (2D) flows in superfluids, such as Bose-Einstein condensates (BECs). In 2D superfluids, a turbulent state can be characterized by a disordered distribution of numerous vortex cores. The question of how to effectively and efficiently generate turbulent states in superfluids is a fundamental question in the field of quantum turbulence. Therefore, experimental studies of vortex nucleation and the onset of turbulence in a superfluid are important for achieving a deeper understanding of the overall problem of turbulence. My PhD dissertation involves the study of vortex nucleation and the onset of turbulence in quasi-2D BECs. First, I discuss experimental apparatus advancements that now enable BECs to be created in a hybrid optical-magnetic trap, an atom trapping configuration conducive to 2DQT experiments. Next, I discuss the design and construction of a quantum vortex microscope and initial vortex detection tests. Finally, I present the first experiments aimed at studying 2DQT carried out in the updated apparatus. Thermal counterflow in superfluid helium, in which the normal and superfluid components flow in opposite directions, is known to create turbulence in the superfluid. However, this phenomenon has not been simulated or studied in dilute-gas BECs as a possible vortex nucleation method. In this dissertation, I present preliminary data from the first experiments aimed at understanding thermal counterflow turbulence in dilute-gas BECs.